Less conservative H2/H∞ design of dynamic output-feedback controllers via LMI´s

In this paper a new method for designing optimal ℋ₂/ℋ_∞ dynamic output-feedback controllers is presented. Due to the use of a path-following method, all bilinear matrix inequalities (BMI´s), which appear typically in this kind of problems, are converted to linear matrix inequalities (LMI´s). The design occurs in two phases. In the first one, a suboptimal, mixed-objective, dynamic output-feedback controller is synthesized. This controller constitutes then the initial step of the computation of an optimal ℋ₂/ℋ_∞ dynamic output-feedback controller, computation which represents the second phase of the design process. The path-following method used in this phase makes it possible to use two different Lyapunov matrices in the two objective constraints, thus reducing the conservatism inherent to other approaches for such a design.